What is the difference in surface areas, in square feet, of the two boxes?
Rectangular Prism: 3 ft by 4.5 ft by 2 ft
Cube: 3 ft

Answer: He is badly mistaken! It's 4/1000

Larry needs to learn how to read percentages!

Step-by-step explanation:

4/10 would be 40%  For every 100 guests, 40 free tickets would be given away. A very popular offer, but the hotel will soon be out money, and out of business!

0.4% is less than 1% . As a decimal it is 0.004. That is Four thousandths!

Only 4 out of every 1000 people were given free round trip tickets to Hawaii.

Answer:

[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]  

[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]  

And the best option for this case would be:

A. 0.050 to 0.112.

Step-by-step explanation:

Data given

[tex]p_A[/tex] represent the real population proportion of who support the cnadite for the northern half state  

[tex]\hat p_A =\frac{1062}{2000}=0.531[/tex] represent the estimated proportion of who support the candidate for the northern half state  

[tex]n_A=2000[/tex] is the sample size required the northern half state  

[tex]p_B[/tex] represent the real population proportion of who support the candidate for the southern half state  

[tex]\hat p_B =\frac{900}{2000}=0.45[/tex] represent the estimated proportion of people who support the candidate for the southern half state  

[tex]n_B=2000[/tex] is the sample size for the northern half state  

[tex]z[/tex] represent the critical value

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]  

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile in the normal standard distribution and we got.  

[tex]z_{\alpha/2}=1.96[/tex]  

Replacing into the formula we got:

[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]  

[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]  

And the best option for this case would be:

A. 0.050 to 0.112.

Answer:

[tex]50\sqrt{2} feet[/tex]

Step-by-step explanation:

Given the vertices  (1, 5) and (11, 15) for the corners labeled with red stars, the diagonal of the square C will be the length of the line joining the two vertices.

Using the Distance Formula:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(1, 5) \:and\: (x_2,y_2)=(11, 15)[/tex]

[tex]Distance=\sqrt{(11-1)^2+(15-5)^2}\\=\sqrt{10^2+10^2}\\=\sqrt{200}\\=10\sqrt{2}[/tex]

Since 1 Square Unit = 25 Square Feet

1 Unit =5 feet

Therefore, the length of the diagonal

[tex]=5*10\sqrt{2} \\=50\sqrt{2} \:feet[/tex]

Answer:

50 with 2 squared

Step-by-step explanation:

Step-by-step explanation:

No of miles Newberg is north of airport = 5

No of miles Rockport is east of the airport = 12

No of miles Newberg and Rockport are apart = 12+5 =17

Answer:

I did this now and was not  12 it was 13

Answer:

u know this carol

Step-by-step explanation:

The height of the rectangle in inches is 6.5 inches.

The area of a rectangle  = lw

where

l = length

w = width

Therefore,

area = 45.5 in²

length = 7 inches

The height of the rectangle can be found below:

45.5 = 7h

divide both sides by 7

45.5 / 7 = h

h = 6.5 inches

learn more: https://brainly.com/question/22713030?referrer=searchResults

Based on the information given the height of the rectangle in inches is 6.5 inches.

Using this formula

Area of a rectangle  = Length× Width

Where:

Area = 45.5 in²

Length = 7 inches

Hence,

Let solve for Length

45.5 = 7h

Divide both sides by 7

h=45.5 / 7  

h = 6.5 inches

Inconclusion the height of the rectangle in inches is 6.5 inches.

Learn more about Area of a rectangle here:https://brainly.com/question/14383947

Answer:

$332.82

Step-by-step explanation:

We will use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, we change 3.4% into a decimal:

3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

[tex]A=200(1+\frac{0.034}{12})^{12(15)}[/tex]

[tex]A=332.82[/tex]

Your balance after 15 years will be $332.82

Answers and Step-by-step explanations:

A. He shared $0.

B. Richie Rich started out with $12. He ended his day with a dozen bucks. However, notice that a dozen is the same as 12, so he still has $12. In other words, he didn't share any money today, so he shared $0.

Hope this helps!

Answer:

A. 0

B. No difference in starting and ending amounts

Step-by-step explanation:

12 = 1 dozen

12 bucks is equal to 1 dozen bucks, which means he didn't spend/share any

Final answer:

To determine how many 2/3s fit into 3/8, multiply 3/8 by the reciprocal of 2/3, resulting in 9/16, which is less than 1. Thus, there are around 0.5625 of 2/3 in 3/8.

Explanation:

To find how many 2/3s are in 3/8, we're essentially asking how to divide 3/8 by 2/3. This is done by multiplying 3/8 by the reciprocal of 2/3, which is 3/2:

Dividing fractions: (3/8) ÷ (2/3) = (3/8) × (3/2)

Multiplying fractions: (3 × 3) / (8 × 2) = 9/16

To simplify this and understand the proportion, we need to compare the fraction 9/16 to a whole number. Since 9/16 is definitely less than 1, there is less than one 'whole' 2/3 in 3/8. Therefore, there are somewhat around 0.5625 of 2/3 in 3/8 (since 9 divided by 16 equals 0.5625).

The shape of the cross-section of the cake is a square.

In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher- dimensional spaces. Cutting an object into slices creates many parallel cross-sections.

Given that, a cake was sliced parallel to the base, we need to find the shape of the cross section,

we see that the shape of the cake is a square base pyramid,

That means if we cut it horizontally parallel to its base, we will always find a square,

Therefore, the cross-section is a square.

Hence, the shape of the cross-section of the cake is a square.

Learn more about cross-section, click;

https://brainly.com/question/15541891

#SPJ3

When slicing a cake parallel to its base, the resulting cross-section will be a circle, mirroring the shape of the base of the cake.

The question pertains to the shape of the cross-section resulting from slicing a cake parallel to its base. When you slice a three-dimensional object like a cake in this way, the cross-section will mirror the shape of the object's base. As the base of a cake is typically a circle, the cross-section in this case will be a circular shape. To understand this better, imagine a cylinder, which is similar to a circular cake. When you slice a cylinder parallel to its base, you always obtain a circular cross-section. This concept is consistent across different objects, given that the slice is parallel to the base, such as slicing a cylindrical polony or cutting a slice of brick-shaped bread.

Boxplots clearly show the five-number summary of a data set. Therefore, option D and E are the correct answer.

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

A) A histogram has an appearance similar to a vertical bar chart, but there are no gaps between the bars.

B) Both dot plots and stem plots can show symmetry, gaps, clusters, and outliers.

C) A bar chart or pie chart is often used to display categorical data. These types of displays, however, are not appropriate for quantitative data. Quantitative data is often displayed using either a histogram, dot plot, or a stem-and-leaf plot.

D) The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets.

E) A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

Therefore, option D and E are the correct answer.

Learn more about the histogram here:

https://brainly.com/question/14421716.

#SPJ5

Among the listed statements, options C and E are true. Other statements about histograms, dotplots, and stemplots have inaccuracies.

Let's go through each of the statements:

(A) Histograms have gaps between each bar: This statement is false as histograms present continuous data where the bars are adjacent to each other with no gaps. It's used for displaying large, continuous, quantitative datasets.

(B) Dotplots do not provide enough information to determine if there are outliers in the data: We can't completely conclude this as it would depend on the nature of the data and how it's presented. Dotplots can sometimes show outliers but they are not the most efficient graph for this purpose.

(C) Bar graphs can display both quantitative and categorical data: This is true. Bar graphs are very versatile and can represent both types of data. They compare categories of data with either horizontal or vertical bars.

(D) Stemplots are the best graphs for displaying data sets with two variables: This is false. Stemplots are good for displaying a single variable and summarizing the shape of the dataset.

(E) Boxplots clearly show the five-number summary of a data set: This is true. Boxplots are an excellent way to display the minimum, first quartile, median, third quartile and maximum values of a data set.

https://brainly.com/question/31524512

#SPJ13

X > 0

sdjkfgsdjfjkdfnejnwsfjdnsk it made me write more

Since the blue line points to numbers more positive then 0, it would be a greater then. Since the dot is open it would be greater then and not equal to.

Therefore the answer is B, x > 0

Answer:

A) (380, 640)

B) ship Tiger: Time = 0.96 hours

Ship Lion: Time = 0.62 hours

C) Ship Tiger = 57.6 minute

Ship Lion = 37.2 minutes

D) Distance = 533 metres

E) Ship Tiger (0, 795)

Ship Lion (1039,0)

Step-by-step explanation:

From the question, we can form the equation of the straight line from the initial and final position of the two ships. Using the general linear equation Y = mx + c. that is

Ship Tiger

Initial position (0, 795)

Final position (1229, 0)

M = (0 - 1229)/795

M = - 1.55

1229 = -1.55(0) + C

C = 1229

Hence the equation of the line for ship Tiger will be

Y = - 1.55x + 1229 ...... (1)

Ship Lion

Initial position (985, 0).

Final position (0, 1039).

M = 1039/ -985 = - 1.05

0 = -1.05(985) + C

0 = - 1039 + C

C = 1039

The equation of the line for ship Lion will be

Y = - 1.05(x) + 1039..... (2)

At the point of intersection of the paths of the ships, they will have common Y and X. Hence equation 1 is equal to equation 2

- 1.55x + 1229 = -1.05(x) + 1039

1.55(x) - 1.05(x) = 1229 - 1039

0.5x = 190

X = 190/0.5 = 380

Substitute x in equation 1

Y = -1.55(380) + 1229

Y = -589 + 1229

Y = 640

Therefore the point of intersection of the paths of the ships is (380, 640)

B) given that Lion will reach her destination in one hour, Tiger – in two hours.

Ship Tiger

distance = root(795^2 + 1229^2)

Distance = 1463.7

Speed = distance/time

Speed = 1463.7/2 = 731.9 m/s

Distance at the point of intersection will be

Distance = root(380^2 + (640-1229)^2)

Distance = root(144400 + 346921)

Distance = 700.9

Speed = distance/time

Time = distance /speed

Time = 700.9/731.9

Time = 0.96 hours

Ship Lion

distance = root(985^2 + 1039^2)

Distance = 1431.69

Speed = distance/time

Speed = 1431.69/1 = 1431.69

Distance at the point of intersection will be

Distance = root((380 - 985)^2 + (640)^2)

Distance = root(775625)

Distance = 880.7 meters

Speed = distance/time

Time = distance /speed

Time = 880.7/1431.69

Time = 0.615 hours

C) the time in minute the distance between Lion and Tiger will be the shortest will be

Ship Tiger: 0.96 × 60 = 57.6 minute

Ship Lion: 0.62 × 60 = 36.9 minutes

D) The shortest distance between Lion and Tiger will be achieved by using pythagorean theorem for the the distances at the point of intersection

Root (880.7^2 - 700.9^2)

Distance = 533 metres

E) the positions of both ships at the moment when the distance between them is the shortest will be the initial position of both ships

That is

Ship Tiger

Initial position (0, 795)

Ship Lion

Initial position (985, 0).

Answer:

[tex] Test score_i= 557.8 +36.42 Income[/tex]

If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:

[tex] Test score_f = 557.8  + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]

And the net increase can be founded like this:

[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]

So then the net increase would be:

C. 0.36 points

Step-by-step explanation:

For this case we have the following linear relationship obtained from least squares between test scores and the student-teacher ratio:

[tex] Test score_i= 557.8 +36.42 Income[/tex]

If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:

[tex] Test score_f = 557.8  + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]

And the net increase can be founded like this:

[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]

So then the net increase would be:

C. 0.36 points

For a 1% increase in income, the test scores would increase by approximately 0.36 points based on the given regression equation. This is calculated by multiplying the coefficient of the natural logarithm of income, 36.42, with the decimal value of the percent change in income, which is 0.01.

The equation provided is a linear regression equation where the dependent variable, TestScore, is predicted based on the natural logarithm of the independent variable, Income. The coefficient of 36.42 in front of the natural logarithm indicates how much the dependent variable changes for a 1% change in the independent variable. To find the contribution to the test scores for a 1% increase in income, we need to use the fact that the derivative of the natural logarithm, Ln(x), with respect to x is 1/x, which means a change in income translates directly to the change in test score when multiplied by the coefficient.

So, for a small percentage change in income, approximately 1%, the corresponding change in TestScore is 36.42 multiplied by the percentage change in decimal form. Specifically, 0.01 × 36.42 = 0.3642 or approximately 0.36 points.

Answer:

2.9106

Step-by-step explanation:

According to the information of the problem

Year 75   76   77   78    79    80    81      82 83 84 85 86 87

Lean 642 644 656  667   673  688 696  698 713 717 725 742 757

If you use a linear regressor calculator you find that approximately

[tex]y = 9.318 x - 61.123[/tex]

so you just find [tex]x = 18[/tex]  and then the predicted value would be 106mm

therefore the predicted value for the lean in 1918 was 2.9106

The probability that the first digit of a three-digit locker combination is less than 3 is 2/9, because there are 2 favorable digits (1 and 2) out of 9 possible non-zero digits, option C.

The question is asking about the probability that the first digit of a three-digit locker combination is less than 3, given that none of the digits can be 0. Since the digits can range from 1 to 9 (inclusive), there are a total of 9 possible digits for the first position. We are interested in the digits 1 and 2, which are the only digits less than 3. Therefore, there are 2 favorable outcomes.

To calculate the probability, we use the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is 2 (favorable outcomes) divided by 9 (possible outcomes), which simplifies to:

Probability = 2/9, option C.

Answer:

We conclude that the average time someone spends in the gym is different from 56 minutes.

Step-by-step explanation:

We are given that UCF believes that the average time someone spends in the gym is 56 minutes.

The university statistician takes a random sample of 32 gym goers and finds the average time of the sample was 50 minutes. Assume it is known the standard deviation of time all people spend in the gym is 8 minutes.

Let [tex]\mu[/tex] = population average time someone spends in the gym

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 56 minutes   {means that the average time someone spends in the gym is 56 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 56 minutes   {means that the average time someone spends in the gym is different from 56 minutes}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

                         T.S.  = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where,  [tex]\bar X[/tex] = sample average time someone takes in the gym = 50 min

              [tex]\sigma[/tex] = population standard deviation = 8 minutes

              n = sample of gym goers = 32

So, test statistics  =   [tex]\frac{50-56}{\frac{8}{\sqrt{32} } }[/tex]

                               =  -4.243

Since in the question we are not given the level of significance so we assume it to b 5%. Now at 5% significance level, the z table gives critical value between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the average time someone spends in the gym is different from 56 minutes.

Answer: 55

Step-by-step explanation:

Answer:

42,43,46,46,49,52,52,55,56

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

let the money on bet is X.

probability of winning =18/38=9/19

probability of losing =(1-9/19)=10/19

expected outcome =[tex]\tiny \sum[/tex]probability *return   =(

Expected value of return after one bet is =(9/19*x)-(10/19*x)=-1x/19

it is negative which is obvious cause casinos are there to earn money.

a) Our best strategy in this case as probability of winning is near by 50 %, we should place a bet of 1 $ each,and when we lose one bet consecutively we should bet twice the amount..

Cause two consecutive losses on black has less probability.

c) In case we have to reach 30 $ we have to use the same strategy as above.

Explaining the best gambling strategy using expected value in roulette scenarios.

Expected value is a key concept when determining the best strategy in gambling scenarios like this. In the given situation, if you want to play until you reach $20 starting with $10, the best strategy is to bet the maximum amount on each spin. This way, your expected value increases, giving you a higher chance of reaching $20.

On the other hand, if you aim to reach $30 starting with $10, it's better to bet smaller amounts on each spin to minimize the risk of going broke quickly. By betting conservatively, you increase your chances of eventually reaching $30.

Answer:

1/52

2/52

4/52

Step-by-step explanation:

If you randomly draw a card from the standard deck the drawing an specific card will have a probability of 1/52

If you  draw a black 2 it can be from Spades 2,  or Clubs 2,  therefore you have only two options, and the probability is  2/52

If you draw an ace it can be spades, clubs, hearts or diamonds, so the probability would be 4/52

Answer:

5 ( 2 + 3x )

Step-by-step explanation:

1st step: Take the GCF of the equation 10+15x

2nd step: GCF means, taking the Greatest Common Factor out of BOTH the numbers in an equation. (GCF is 5 in this case.)

3rd step: Divide by the GCF that you got. (In this case, you have 10 +15x. You need to do 10/5, and 15x /5. (Note that ANYTHING multiplied by "x" can also be divided just like a regular number.)

4th step: Put the the number that you divided with for both numbers OUTSIDE parentheses. (Note in this case it is common.)

5th step: Check your work. PLEASE DO THIS STEP.

Check: 5( 2 + 3x )

5 x 2 = 10

5 x '3x' = 15x

So, the answer for this problem is: 5 ( 2 +3x )

Answer: 5( 2 + 3x)

Hope this helped you understand the basics of disributive property. And if you have another problem just like this, you can use the same rule as shown above. :)

Final answer:

Use the distributive property to factor out a common factor in 10 + 15x to get an equivalent expression.

Explanation:

To write an expression equivalent to 10 + 15x using the distributive property, you can factor out a common factor. Here’s how:

Factor out 5 from 10 and 15x: 10 + 15x = 5(2 + 3x)

Apply the distributive property to get the equivalent expression: 5(2 + 3x) = 5*2 + 5*3x = 10 + 15x

Answer:

(2x)(-2x+5)(x+2)

Step-by-step explanation:

Answer:

The mean waiting time of all customers is significantly more than 3 minutes, at 0.05 significant level

Step-by-step explanation:

Step 1: State the hypothesis and identify the claim.

[tex]H_0:\mu=3\\H_1:\mu\:>\:3(claim)[/tex]

Step 2: We calculate the critical value. Since we were not given any significant level, we assume [tex]\alpha=0.05[/tex], and since this is a right tailed test, the critical value is z=1.65

Step 3: Calculate the test statistic.

[tex]Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }=\frac{3.1-3}{\frac{0.5}{\sqrt{100} } }=2[/tex]

Step 4:Decide. Since the test statistic , 2 s greater than the critical value, 1.65, and it is in the critical region, the decision is to reject the null hypothesis.

Step 5: Conclusion, there is enough evidence to support the claim that the mean is greater than 3

Answer: 1. -16.18

2. 3.75

3. -3

Step-by-step explanation:

The value of the local minimum, maximum, and minimum will be -16, 4, and -1.5.

The larger than the critical value of a set are really the highest and lowest items in the set, as described by mathematics.

From the graph, the conclusion are given below.

Over the interval [-3, 0], the local minimum is approximately -16.

Over the interval [0, 3], the local maximum is approximately 4.

Over the interval [0, 3] the local minimum is approximately -1.5.

The complete question is attached below.

More about the local minima and local maxima link is given below.

https://brainly.com/question/18687565

#SPJ2

Answer:

  in 6 years

Step-by-step explanation:

Using t=10 to represent today, we can write the exponential growth function as ...

  p(t) = 200(550/200)^(t/10)

Then we can set p(t) = 1000 and solve for t:

  1000 = 200(11/4)^(t/10) . . . . simplifying the growth factor

  1000/200 = (11/4)^(t/10) . . . . divide by 200

  log(5) = (t/10)log(11/4) . . . . . . take logs

  t = 10·log(5)/log(11/4) ≈ 15.91

That is, about 16 years from 10 years ago, the population will reach 1000.

The population will reach 1000 in about 6 years.

Answer:

x intercept = (1.2 , 0)

y intercept = (0 , 0.75)

Step-by-step explanation:

You wan to get it into whatever formula makes it easiest for you to understand. I put it into standard slope formula ax + by = c

5x +8y = 6

6/5 = x

x= 1.2

6/8 = y

y = 0.75

Answer:

(a)

x = 2

y = 42.019

(b)

x = 3.5

y = 51.833

(c)

x = 12

y = 107.447

(d)

x = 1.5

y = 38.747

Step-by-step explanation:

If you use a regressor calculator you will find that

y = 6.542x + 28.933

then for (a)

x = 2

y = 42.019

(b)

x = 3.5

y = 51.833

(c)

x = 12

y = 107.447

(d)

x = 1.5

y = 38.747

Regression equations are used to represent scatter plots

The table is given as:

x | 1 2 3 3 4 6

y | 37 41 51 48 65 69

To determine the regression equation, we make use of an graphing calculator.

From the graphing calculator, we have:

The regression equation is represented as:

[tex]\^y =b\^x + a[/tex]

Where:

[tex]b = \frac{SP}{SS_x}[/tex] and [tex]a = M_y - bM_x[/tex]

So, we have:

[tex]b = \frac{SP}{SS_x}[/tex]

[tex]b = \frac{17.5}{114.5}[/tex]

[tex]b = 6.54[/tex]

[tex]a = M_y - bM_x[/tex]

[tex]a = 51.83 - (6.54*3.5)[/tex]

[tex]a = 28.94[/tex]

Substitute values for (a) and (b) in [tex]\^y =b\^x + a[/tex]

[tex]\^y = 6.54\^x + 28.94[/tex]

The predicted values when x = 2, 3.5, 12 and 1.5 are:

[tex]\^y = 6.54 \times 2 + 28.94 = 42.02[/tex]

[tex]\^y = 6.54 \times 3.5 + 28.94 = 51.83[/tex]

[tex]\^y = 6.54 \times 12 + 28.94 = 107.42[/tex]

[tex]\^y = 6.54 \times 1.5 + 28.94 = 38.75[/tex]

Hence, the predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75

Read more about regressions equations at:

https://brainly.com/question/5586207

Answer:

We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%

Step-by-step explanation:

-From the given information, [tex]\hat p=0.65[/tex].

-We calculate the confidence interval using this value at 95% confidence level:

[tex]CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585][/tex]

So, the 95% confidence interval is (0.6515,0.6585).

Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.

Given:

The lengths of the three sides of the triangle are [tex]\frac{3}{x-4}[/tex], [tex]\frac{16-x}{x^{2}-2 x-8}[/tex] and [tex]\frac{x+5}{x+2}[/tex]

We need to determine the perimeter of the triangle.

Perimeter of the triangle:

The perimeter of the triangle can be determined by adding all the three sides.

Thus, we have;

[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{x^{2}-2 x-8}+\frac{x+5}{x+2}[/tex]

Factoring the term [tex]x^2-2x-8[/tex], we get, [tex](x-4)(x+2)[/tex]

Substituting, we get;

[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{(x-4)(x+2)}+\frac{x+5}{x+2}[/tex]

Taking LCM , we have;

[tex]Perimeter=\frac{3(x+2)+16-x+(x+5)(x-4)}{(x-4)(x+2)}[/tex]

Simplifying the numerator, we get;

[tex]Perimeter=\frac{3x+6+16-x+x^2-4x+5x-20}{(x-4)(x+2)}[/tex]

Adding the like terms in the numerator, we get;

[tex]Perimeter=\frac{x^2+3x+2}{(x-4)(x+2)}[/tex]

Factoring the numerator, we get;

[tex]Perimeter=\frac{(x+2)(x+1)}{(x-4)(x+2)}[/tex]

Cancelling the common terms, we have;

[tex]Perimeter=\frac{x+1}{x-4}[/tex]

Thus, the perimeter of the triangle is [tex]\frac{x+1}{x-4}[/tex]